In terms of sound quality, studio monitors surpass the headphones in almost every way. But there is a way that headphones are better.
Because they covering your ears, headphones allow you to hear a lot more fine details in a mix. This makes them ideal for detecting noises such as clicks, pops, etc.
In most home studios, noise is a constant battle. Maybe you are in a noisy neighborhood and it disturbs you during the day.
And at night when everyone is asleep, the idea strikes of you have a mix to finish, the chances are you will disturb the surroundings.
With headphones, everyone gets the peace and quiet to do as they please.
Privacy. As much as we hate to admit it, many of us are self-conscious about our music. Especially when you are nowhere near the finished mix or you are bouncing some crazy ideas.
Knowing that others are listening can be a crippling distraction that kills your creativity. But with headphones, no one hears you, but you.
Freedom of location. With studio monitors, your work is confined a single location. And normally that's fine, except when maybe you're on the road or you need a break from your studio.
With headphones, you can work wherever, whenever you want. And you don't even have to worry about acoustic treatment.
Choosing proper headphones

Unlike most speaker manufacturers, headphone designers do not look for a flat frequency response:
most headphones have a bump of up to 4dB between 40Hz and 500Hz, to compensate for the fact that you are not feeling the low frequencies through your body as you do with speakers.
At frequencies above 1 kHz, they typically have a gradual attenuation (perhaps 5dB at 20 kHz) to compensate for the fact that the drivers are placed directly against your ear.
There are different types of headphones available, and some are more suitable for mixing than others. Planar magnetic headphones are best suited for audio mixing.
The correct term for traditional headphones is circum-aural devices, because they cover the outer ear, while supra-aural types sit on top of the ears and are both available in open, closed and semi-open back versions.
Open-back designs have grids that expose the sound to the outside world, which reduces the resonance effects and inherently provides cross-feed between the ears, giving these designs a more natural and "airy" sound while mixing.
However, they are not the best choice for performers during tracking because their sound will spill into your microphone recordings.
Closed-back are much better suited for this purpose, and they are also better for mixing when you're in a noisy environment and want to block the world. You can also read, best noise isolating earbuds.
However, this insulation can also lead to moist ears, making closed-back headphones less suitable for long mixing sessions.
Nevertheless, for mixing, the majority of recommended models tend to be open-backed headphones for comfort and cool ears for long mixing sessions and circum-aural for the deepest and most natural bass.
The Sennheiser HD650 are very popular in audio circles due to their incredibly detailed and neutral sound of their low frequency.
For those who that the sound of the HD650 is not quite enough, the Grado RS2 might be more apt to expose details a bit more meticulously, while others say that the K701 from AKG presents the cleanest sound.
Mixing with headphones – tips
1. Protect your ears
If you are using headphones, you realize there is a risk that the hearing loss is greater than when you use studio monitors, because the drivers are positioned right next to your ears.
Because using headphones can be very immersive and mixing is often a time-consuming process, it is important to take regular breaks to avoid hearing fatigue.
Keep track of the SPL volume and how long you spend mixing, to avoid accidentally damaging your hearing.
So, if your SPL volume is at 85dB the standard recommendation is 8 work hours, as you increase the SPL by 3dB you have to decrease the work time by double. For example SPL 88dB / 4 hours; SPL 91dB / 2 hours, etc.
2. Learn your equipment on mixes you are quite familiar
Keep in mind that when you mix with headphones, to avoid trying to make the track sound good on that particular headset, but create a mix that will have a good impact on different playback systems.
This can be difficult because the physics of the headphones makes it almost impossible to generate the full frequency spectrum.
Bass sounds require significant space for waveforms to develop, and headphones lack most of the spatial information necessary for stereo image processing and reverberation.
To make a mix to sound like you want on other systems, it is useful to keep a catalog of reference tracks that you know well.
For example, imagine that you are working on a "bass" on a piece of electronic music and you want it to be as close as possible to a track that you really familiar.
Listen to the reference track through your headphones, and work on the low end on your own mix to make it sound similar to the reference track.
Then, if possible, verify that your mix and the reference mix sounds the same on a pair of near or mid-field studio monitors.
3. Know what to mix in the headphones and what to leave to the studio monitors
Headphones can be very helpful for focusing on precise details and correcting errors from individual tracks.
Clarity and isolation from acoustic coloration can make it easier to detect and fix problems with saturation, cracking, pops and clicks, and dynamic signal processing, such as compression, can be achieved more precisely on individual tracks.
In addition, headphones are not as good for tone-shaping processes, such as EQ and reverb, because the frequency response of the sound varies with the distance from the source and acoustic properties of different rooms.
Unless you choose to invest in hardware or software for acoustic signal-processing, it is probably best to limit the headphone mixing to correct individual track errors and leave the others processes such as imaging, tone-shaping, reverb processing and low end for a time when you can use studio monitors.
Plug-ins for proper headphone monitoring

Now I will give you a list of headphone monitor plug-ins that have unique feature sets and technologies which claim to provide more natural experience.
Waves NX: There have been other attempts to transfer the auditory experience from the speaker to the headphones, but many have not been able to compensate for the position and movement of the head.
On the headphones, the soundstage follows every movement of our heads. This is not the case with loudspeakers, where changing the sounds we hear as we move is essential to determine the direction from where the sound originates.
That's where the Waves Nx head tracking technology comes from.
This can follow the movement of the user's head, either with the camera built into the computer, or even better with the dedicated Waves Nx Head Tracker, which clips on your headphones with a thick rubber band and communicates with the computer via Bluetooth.
The Nx Head Tracker works in low light and when you're not exactly in front of the computer, it reacts faster to the movements of the head than to the camera.
For greater precision and speed, it is possible to combine the inputs of the main tracker and the camera.
Isone By Toneboosters: It offers some similar features to Waves NX without the head tracking technology. Isone then is a static approach to mix room emulation.
Sadly for Pro Tools users, Isone is AU and VST only but I got around this by using PatchWork by Blue Cat Audio to host the VST in Pro Tools.
With Isone, a stereo virtual reproduction system and the listening room can now be experienced simply using high-quality headphones.
The frequency response and the directivity pattern of the loudspeakers can be adjusted.
Furthermore, the reverb time and volume of the virtual listening room and the distance to the virtual loudspeakers can be fully customized.
Reference 3 by Sonarworks: It provides audio engineers with a set of tools designed to quickly deliver reference sound in the studio or on the road, by ridding speakers from room coloration, and adjusting the frequency response of selected headphones to precisely match flat and neutral-sounding studio monitors, in a well-treated studio.
This allows for critical listening and helps ensure that your mixes translate more accurately when played on other monitoring systems.
In addition, the Reference 3 Systemwide calibration software allows you to hear how your tracks sound on a variety of music delivery platforms such as Spotify, Youtube, Soundcloud, and more.
Conclusion
In general, it is quite possible to do most of you mixing with headphones, provided that they can be occasionally checked on the speakers and improved for both playback systems.
If this makes your music more appealing to many mp3 player users, then it's even better. Remember that many potential buyers will listen to your songs with their headphones.